Equipped with the optimal plan \(\pi ^{\ast }\) , we transport the embeddings of the support set \(\phi (x_{s,i})\)  to \(\hat{z}_{s,i}\)  by barycenter mapping [1]} to adapt the support set to the query set.
\(\small \hat{\phi }(x_{s,i}) =\frac{\sum _{x_{q,j}\in \mathcal {Q}}\pi ^{\ast }(x_{s,i},x_{q,j}) \phi (x_{q,j}) }{ \sum _{x_{q,j}\in \mathcal {Q}}\pi ^{\ast }(x_{s,i},x_{q,j})}.\) 
